Studor vent distance?

Hello, I'm in process of finishing a bathroom in basement using existing plumbing. The plumbing was stubbed but no vent was installed and tapping into vent upstairs would be pretty hard. I talked to the plumber who installed the plumbing and he says the use of studor vents (AAV) is allowed in our county. My question is, is there a limited distance? I've included some pics. My vanity is to the right and I need to tie into the 2" pipe sticking out behind the toilet drain. If I ran a 2" pipe along the wall to the existing pipe and installed a studor vent under the vanity, would that be enough for proper venting? Or should I install a 'T' on top of the existing plumbing where I'm going to tie into and install a studor vent on top of the tee as well as under the vanity. straight line distance from vanity to drain is 8'. but the horizontal distance to run from vanity to drain along the wall is 12'. Thanks for the help

Studor vent distance?

Studor vent distance?

Thanks for the response guys. The AAV will be accesible, it will be located behind the vanity door. I was just making sure I would not need another one since the AAV vent will be 12 feet away from the toilet drain. This vent will be the vent for all 3 fixtures. Sink, toilet, shower